Question: What is the largest possible median for the five number set        $\{x, 2x, 3, 2, 5\}$ if $x$ can be any integer?
Answer: The median is the number in the set with half the other numbers larger than it and half the others smaller. To maximize the median, we need to make $x$ as large as possible, so the items $x$ and $2x$ are as large as possible. Then, the median is $\boxed{5}$, since 3 and 2 (half the other members) are smaller than it and $x$ and $2x$ are larger than it.